Chapter 4.3, Problem 18E

Reminder Round all answers to two decimal places unless otherwise indicated.

Wages A worker is reviewing his pay increases over the past several years. The table below shows the hourly wage $W$, in dollars, that he earned as a function of time $t$, measured in years since the beginning of 2000.

Time $t$	Wages $W$
$1$	$15.30$
$2$	$15.60$
$3$	$15.90$
$4$	$16.25$

a. By calculating ratios, show that the data in this table are exponential. (Round the quotients to two decimal places)

b. What is the yearly growth factor for the data?

c. The worker can't remember what hourly wage he earned at the beginning of 2000. Assuming that $W$ is indeed an exponential function, determine what that hourly wage was?

d. Find a formula giving an exponential model for $W$ as a function of $t$.

e. What percentage raise did the worker receive each year?

f. Given that prices increased by 26% over the decade of the 2000s your model to determine whether the workers wage increases kept pace with inflation.